Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 335.6 | ||
Character | \(\chi\) | \(=\) | 432.335 |
Dual form | 432.2.be.a.383.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.64221 | − | 0.550590i | 0.948130 | − | 0.317884i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00608 | + | 2.76418i | −0.449932 | + | 1.23618i | 0.482839 | + | 0.875709i | \(0.339606\pi\) |
−0.932771 | + | 0.360469i | \(0.882617\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.201339 | + | 0.0355015i | 0.0760989 | + | 0.0134183i | 0.211568 | − | 0.977363i | \(-0.432143\pi\) |
−0.135469 | + | 0.990782i | \(0.543254\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.39370 | − | 1.80837i | 0.797900 | − | 0.602790i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.91100 | − | 1.05952i | 0.877700 | − | 0.319457i | 0.136419 | − | 0.990651i | \(-0.456441\pi\) |
0.741281 | + | 0.671195i | \(0.234219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23448 | − | 1.03585i | 0.342382 | − | 0.287293i | −0.455340 | − | 0.890318i | \(-0.650482\pi\) |
0.797723 | + | 0.603025i | \(0.206038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.130261 | + | 5.09330i | −0.0336333 | + | 1.31508i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.86450 | + | 1.65382i | −0.694743 | + | 0.401110i | −0.805386 | − | 0.592750i | \(-0.798042\pi\) |
0.110644 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.98415 | + | 3.45495i | 1.37286 | + | 0.792621i | 0.991287 | − | 0.131718i | \(-0.0420495\pi\) |
0.381572 | + | 0.924339i | \(0.375383\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.350187 | − | 0.0525544i | 0.0764171 | − | 0.0114683i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.21573 | + | 6.89473i | 0.253497 | + | 1.43765i | 0.799902 | + | 0.600130i | \(0.204885\pi\) |
−0.546406 | + | 0.837521i | \(0.684004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79827 | − | 2.34802i | −0.559653 | − | 0.469605i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.93529 | − | 4.28767i | 0.564896 | − | 0.825162i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.70909 | + | 3.22857i | −0.503065 | + | 0.599530i | −0.956490 | − | 0.291765i | \(-0.905758\pi\) |
0.453425 | + | 0.891294i | \(0.350202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.173262 | + | 0.0305507i | −0.0311187 | + | 0.00548707i | −0.189186 | − | 0.981941i | \(-0.560585\pi\) |
0.158067 | + | 0.987428i | \(0.449474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.19711 | − | 3.34272i | 0.730623 | − | 0.581893i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.300695 | + | 0.520819i | −0.0508267 | + | 0.0880345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.46424 | − | 9.46434i | −0.898315 | − | 1.55593i | −0.829647 | − | 0.558288i | \(-0.811459\pi\) |
−0.0686675 | − | 0.997640i | \(-0.521875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.45694 | − | 2.38077i | 0.233297 | − | 0.381229i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.982963 | − | 1.17145i | −0.153513 | − | 0.182950i | 0.683807 | − | 0.729663i | \(-0.260323\pi\) |
−0.837320 | + | 0.546713i | \(0.815879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.57898 | − | 9.83317i | −0.545789 | − | 1.49954i | −0.839343 | − | 0.543601i | \(-0.817060\pi\) |
0.293554 | − | 0.955942i | \(-0.405162\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.59040 | + | 8.43598i | 0.386155 | + | 1.25756i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.76136 | − | 9.98915i | 0.256920 | − | 1.45707i | −0.534175 | − | 0.845374i | \(-0.679378\pi\) |
0.791095 | − | 0.611693i | \(-0.209511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.53857 | − | 2.37985i | −0.934082 | − | 0.339978i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.79353 | + | 4.29308i | −0.531200 | + | 0.601152i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.56595i | 0.489820i | 0.969546 | + | 0.244910i | \(0.0787585\pi\) | ||||
−0.969546 | + | 0.244910i | \(0.921242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.11248i | 1.22873i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7295 | + | 2.37894i | 1.55361 | + | 0.315098i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.69955 | − | 1.71050i | −0.611829 | − | 0.222688i | 0.0174743 | − | 0.999847i | \(-0.494437\pi\) |
−0.629303 | + | 0.777160i | \(0.716660\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18103 | − | 6.69796i | 0.151216 | − | 0.857586i | −0.810949 | − | 0.585117i | \(-0.801049\pi\) |
0.962164 | − | 0.272469i | \(-0.0878403\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.546144 | − | 0.279115i | 0.0688077 | − | 0.0351652i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.62129 | + | 4.45446i | 0.201097 | + | 0.552508i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.60404 | − | 3.10337i | −0.318134 | − | 0.379137i | 0.583151 | − | 0.812364i | \(-0.301819\pi\) |
−0.901285 | + | 0.433226i | \(0.857375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.79265 | + | 10.6532i | 0.697353 | + | 1.28250i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.61271 | + | 4.52534i | 0.310071 | + | 0.537059i | 0.978377 | − | 0.206827i | \(-0.0663138\pi\) |
−0.668306 | + | 0.743886i | \(0.732980\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.68403 | + | 8.11298i | −0.548225 | + | 0.949553i | 0.450172 | + | 0.892942i | \(0.351363\pi\) |
−0.998396 | + | 0.0566108i | \(0.981971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.88814 | − | 2.31525i | −0.679904 | − | 0.267342i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.623712 | − | 0.109977i | 0.0710786 | − | 0.0125331i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.13899 | + | 7.31617i | −0.690691 | + | 0.823133i | −0.991439 | − | 0.130570i | \(-0.958319\pi\) |
0.300748 | + | 0.953704i | \(0.402764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.45960 | − | 8.65739i | 0.273289 | − | 0.961932i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.47037 | − | 7.10748i | −0.929743 | − | 0.780147i | 0.0460279 | − | 0.998940i | \(-0.485344\pi\) |
−0.975771 | + | 0.218793i | \(0.929788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.68954 | − | 9.58186i | −0.183256 | − | 1.03930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.67127 | + | 6.79358i | −0.286390 | + | 0.728348i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.64985 | + | 1.52989i | 0.280884 | + | 0.162168i | 0.633823 | − | 0.773478i | \(-0.281485\pi\) |
−0.352940 | + | 0.935646i | \(0.614818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.285322 | − | 0.164731i | 0.0299099 | − | 0.0172685i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.267711 | + | 0.145567i | −0.0277604 | + | 0.0150946i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.5706 | + | 13.0653i | −1.59751 | + | 1.34047i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58670 | + | 0.577510i | −0.161105 | + | 0.0586373i | −0.421314 | − | 0.906915i | \(-0.638431\pi\) |
0.260209 | + | 0.965552i | \(0.416209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.05206 | − | 7.80033i | 0.507752 | − | 0.783963i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.31576 | − | 1.28997i | −0.727946 | − | 0.128356i | −0.202620 | − | 0.979258i | \(-0.564946\pi\) |
−0.525326 | + | 0.850901i | \(0.676057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.55315 | − | 15.2572i | 0.547169 | − | 1.50333i | −0.290348 | − | 0.956921i | \(-0.593771\pi\) |
0.837516 | − | 0.546412i | \(-0.184007\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.207046 | + | 1.02085i | −0.0202056 | + | 0.0996251i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3992 | 1.29535 | 0.647676 | − | 0.761916i | \(-0.275741\pi\) | ||||
0.647676 | + | 0.761916i | \(0.275741\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6377 | 1.40204 | 0.701021 | − | 0.713141i | \(-0.252728\pi\) | ||||
0.701021 | + | 0.713141i | \(0.252728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1844 | − | 12.5339i | −1.34632 | − | 1.18966i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.06668 | + | 16.6681i | −0.570705 | + | 1.56800i | 0.232689 | + | 0.972551i | \(0.425247\pi\) |
−0.803394 | + | 0.595448i | \(0.796975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.2814 | − | 3.57616i | −1.89125 | − | 0.333478i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.08177 | − | 4.71190i | 0.100010 | − | 0.435616i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.635448 | + | 0.231284i | −0.0582514 | + | 0.0212018i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.07514 | + | 0.902150i | −0.0977400 | + | 0.0820136i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.25922 | − | 1.38256i | −0.203707 | − | 0.124661i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.43177 | + | 1.98133i | −0.306947 | + | 0.177216i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.62718 | − | 2.09415i | −0.321860 | − | 0.185826i | 0.330361 | − | 0.943855i | \(-0.392829\pi\) |
−0.652221 | + | 0.758029i | \(0.726163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.2915 | − | 14.1776i | −0.994159 | − | 1.24826i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.37574 | − | 13.4735i | −0.207570 | − | 1.17719i | −0.893345 | − | 0.449372i | \(-0.851648\pi\) |
0.685775 | − | 0.727814i | \(-0.259463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.08219 | + | 0.908062i | 0.0938375 | + | 0.0787390i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.89875 | + | 12.4274i | 0.765883 | + | 1.06958i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.304060 | + | 0.362365i | −0.0259776 | + | 0.0309589i | −0.778877 | − | 0.627177i | \(-0.784210\pi\) |
0.752899 | + | 0.658136i | \(0.228655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9825 | − | 3.69979i | 1.77972 | − | 0.313812i | 0.815465 | − | 0.578806i | \(-0.196481\pi\) |
0.964250 | + | 0.264994i | \(0.0853701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.60741 | − | 17.3741i | −0.219584 | − | 1.46316i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.49606 | − | 4.32331i | 0.208731 | − | 0.361533i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.19878 | − | 10.7366i | −0.514781 | − | 0.891626i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0480 | − | 0.308128i | −0.993704 | − | 0.0254140i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3756 | − | 14.7487i | −1.01385 | − | 1.20826i | −0.977936 | − | 0.208904i | \(-0.933011\pi\) |
−0.0359129 | − | 0.999355i | \(-0.511434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.21217 | + | 11.5729i | 0.342782 | + | 0.941786i | 0.984584 | + | 0.174915i | \(0.0559650\pi\) |
−0.641802 | + | 0.766871i | \(0.721813\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.86604 | + | 9.13882i | −0.312550 | + | 0.738829i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0898674 | − | 0.509663i | 0.00721832 | − | 0.0409371i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0345 | + | 5.47210i | 1.19988 | + | 0.436721i | 0.863183 | − | 0.504892i | \(-0.168468\pi\) |
0.336698 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.96338 | + | 5.85603i | 0.155706 | + | 0.464413i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.43134i | 0.112805i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5222i | 0.980811i | 0.871494 | + | 0.490406i | \(0.163151\pi\) | ||||
−0.871494 | + | 0.490406i | \(0.836849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.01725 | + | 14.9646i | 0.390592 | + | 1.16499i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.06389 | − | 2.20708i | −0.469238 | − | 0.170789i | 0.0965691 | − | 0.995326i | \(-0.469213\pi\) |
−0.565807 | + | 0.824538i | \(0.691435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.80648 | + | 10.2450i | −0.138960 | + | 0.788080i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.5721 | − | 2.55144i | 1.57319 | − | 0.195113i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.34451 | − | 3.69400i | −0.102221 | − | 0.280850i | 0.878031 | − | 0.478605i | \(-0.158857\pi\) |
−0.980252 | + | 0.197755i | \(0.936635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.480041 | − | 0.572091i | −0.0362877 | − | 0.0432460i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.65942 | − | 0.221465i | −0.650882 | − | 0.0166463i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2327 | + | 22.9198i | 0.989061 | + | 1.71310i | 0.622276 | + | 0.782798i | \(0.286208\pi\) |
0.366785 | + | 0.930306i | \(0.380458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.77259 | + | 4.80227i | −0.206085 | + | 0.356950i | −0.950478 | − | 0.310792i | \(-0.899406\pi\) |
0.744393 | + | 0.667742i | \(0.232739\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.74833 | − | 11.6497i | −0.129241 | − | 0.861172i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.6586 | − | 5.58226i | 2.32758 | − | 0.410416i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.58631 | + | 7.84925i | −0.481638 | + | 0.573994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.743205 | − | 0.759067i | 0.0540602 | − | 0.0552140i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.21805 | − | 6.05666i | −0.522280 | − | 0.438245i | 0.343146 | − | 0.939282i | \(-0.388507\pi\) |
−0.865426 | + | 0.501037i | \(0.832952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.81540 | + | 15.9670i | 0.202657 | + | 1.14933i | 0.901084 | + | 0.433645i | \(0.142773\pi\) |
−0.698427 | + | 0.715682i | \(0.746116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.11508 | + | 6.42249i | 0.366299 | + | 0.459924i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4926 | − | 7.21263i | −0.890063 | − | 0.513878i | −0.0161001 | − | 0.999870i | \(-0.505125\pi\) |
−0.873963 | + | 0.485992i | \(0.838458\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.37317 | + | 1.94750i | −0.239118 | + | 0.138055i | −0.614771 | − | 0.788705i | \(-0.710752\pi\) |
0.375653 | + | 0.926760i | \(0.377418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.98506 | − | 3.66263i | −0.422154 | − | 0.258342i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.660064 | + | 0.553859i | −0.0463274 | + | 0.0388733i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.22704 | − | 1.53852i | 0.295229 | − | 0.107455i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.3783 | + | 14.3054i | 1.06887 | + | 0.994297i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0805 | + | 3.71705i | 1.45817 | + | 0.257114i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.01625 | − | 19.2770i | 0.483018 | − | 1.32708i | −0.423874 | − | 0.905721i | \(-0.639330\pi\) |
0.906893 | − | 0.421361i | \(-0.138448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.78222 | + | 5.99302i | 0.464710 | + | 0.410635i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.7814 | 2.09927 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0359689 | −0.00244173 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.22523 | + | 15.9022i | −0.217941 | + | 1.07457i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.82305 | + | 5.00879i | −0.122632 | + | 0.336928i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.04386 | − | 0.889368i | −0.337762 | − | 0.0595565i | 0.00219496 | − | 0.999998i | \(-0.499301\pi\) |
−0.339957 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.9443 | − | 0.560168i | −0.729621 | − | 0.0373446i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.64745 | + | 0.963595i | −0.175718 | + | 0.0639560i | −0.428381 | − | 0.903598i | \(-0.640916\pi\) |
0.252663 | + | 0.967554i | \(0.418694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.12439 | + | 5.97807i | −0.470793 | + | 0.395042i | −0.847084 | − | 0.531459i | \(-0.821644\pi\) |
0.376291 | + | 0.926502i | \(0.377199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.963713 | − | 0.524015i | 0.0634076 | − | 0.0344777i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.4589 | − | 11.8120i | 1.34031 | − | 0.773828i | 0.353458 | − | 0.935451i | \(-0.385006\pi\) |
0.986853 | + | 0.161622i | \(0.0516726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8397 | + | 14.9186i | 1.68560 | + | 0.973180i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.05330 | + | 15.3947i | −0.393204 | + | 0.999996i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.21197 | + | 18.2160i | 0.207765 | + | 1.17829i | 0.893029 | + | 0.449999i | \(0.148576\pi\) |
−0.685264 | + | 0.728295i | \(0.740313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.33009 | + | 1.95517i | 0.150094 | + | 0.125944i | 0.714743 | − | 0.699388i | \(-0.246544\pi\) |
−0.564649 | + | 0.825331i | \(0.690988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.727493 | − | 15.5715i | −0.0466687 | − | 0.998910i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1566 | − | 15.6795i | 0.840547 | − | 1.00172i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9661 | − | 1.93362i | 0.697757 | − | 0.123033i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.8234 | − | 7.00827i | −1.12951 | − | 0.444131i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.32283 | + | 2.29121i | −0.0834963 | + | 0.144620i | −0.904749 | − | 0.425944i | \(-0.859942\pi\) |
0.821253 | + | 0.570564i | \(0.193275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8441 | + | 18.7825i | 0.681761 | + | 1.18084i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.05026 | − | 14.8052i | −0.504127 | − | 0.927135i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.61198 | − | 11.4551i | −0.599579 | − | 0.714551i | 0.377838 | − | 0.925872i | \(-0.376668\pi\) |
−0.977417 | + | 0.211321i | \(0.932223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.764165 | − | 2.09953i | −0.0474829 | − | 0.130458i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.646307 | + | 12.6273i | −0.0400054 | + | 0.781607i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.11650 | − | 23.3458i | 0.253834 | − | 1.43957i | −0.545213 | − | 0.838298i | \(-0.683551\pi\) |
0.799047 | − | 0.601268i | \(-0.205338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.85691 | − | 3.58762i | −0.605505 | − | 0.220386i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.19396 | + | 1.05342i | 0.317865 | + | 0.0644683i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.9967i | − | 1.09728i | −0.836060 | − | 0.548638i | \(-0.815146\pi\) | ||
0.836060 | − | 0.548638i | \(-0.184854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.89090i | − | 0.418592i | −0.977852 | − | 0.209296i | \(-0.932883\pi\) | ||
0.977852 | − | 0.209296i | \(-0.0671173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.377860 | − | 0.427618i | 0.0228691 | − | 0.0258806i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.6335 | − | 3.87029i | −0.641226 | − | 0.233387i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.940086 | + | 5.33149i | −0.0564843 | + | 0.320338i | −0.999938 | − | 0.0111670i | \(-0.996445\pi\) |
0.943453 | + | 0.331505i | \(0.107556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.359490 | + | 0.386451i | −0.0215221 | + | 0.0231362i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.04984 | − | 16.6218i | −0.360903 | − | 0.991573i | −0.978711 | − | 0.205244i | \(-0.934201\pi\) |
0.617808 | − | 0.786329i | \(-0.288021\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.98533 | + | 4.74953i | 0.236903 | + | 0.282330i | 0.871377 | − | 0.490614i | \(-0.163228\pi\) |
−0.634474 | + | 0.772944i | \(0.718783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.3766 | + | 30.0290i | −1.08854 | + | 1.77877i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.156320 | − | 0.270755i | −0.00922731 | − | 0.0159822i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.02977 | + | 5.24771i | −0.178222 | + | 0.308689i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.28772 | + | 1.82201i | −0.134108 | + | 0.106808i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7111 | − | 2.24131i | 0.742589 | − | 0.130938i | 0.210461 | − | 0.977602i | \(-0.432504\pi\) |
0.532128 | + | 0.846664i | \(0.321392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.45623 | − | 11.2695i | 0.550563 | − | 0.656135i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00176 | − | 15.5914i | 0.232206 | − | 0.904704i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.64269 | + | 7.25208i | 0.499820 | + | 0.419399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.371496 | − | 2.10686i | −0.0214127 | − | 0.121437i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.7243 | + | 1.90959i | −0.730989 | + | 0.109703i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.3262 | + | 10.0033i | 0.992093 | + | 0.572785i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4699 | + | 7.19947i | −0.711692 | + | 0.410896i | −0.811687 | − | 0.584092i | \(-0.801451\pi\) |
0.0999951 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.718990 | − | 28.1130i | 0.0409019 | − | 1.59929i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.88767 | + | 4.94034i | −0.333859 | + | 0.280141i | −0.794270 | − | 0.607565i | \(-0.792146\pi\) |
0.460411 | + | 0.887706i | \(0.347702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.11474 | + | 2.22558i | −0.345625 | + | 0.125797i | −0.508999 | − | 0.860767i | \(-0.669984\pi\) |
0.163374 | + | 0.986564i | \(0.447762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.222059 | + | 1.79045i | 0.0125116 | + | 0.100881i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.2668 | − | 3.39726i | −1.08213 | − | 0.190809i | −0.395974 | − | 0.918262i | \(-0.629593\pi\) |
−0.686158 | + | 0.727452i | \(0.740704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.46544 | + | 12.2687i | −0.250016 | + | 0.686915i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.0043 | − | 7.37749i | 1.22816 | − | 0.411771i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8555 | −1.27171 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.88660 | −0.326530 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.0382 | − | 8.05940i | 1.32932 | − | 0.445686i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.709259 | − | 1.94867i | 0.0391027 | − | 0.107434i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5610 | − | 4.33077i | −1.35000 | − | 0.238041i | −0.548555 | − | 0.836114i | \(-0.684822\pi\) |
−0.801441 | + | 0.598073i | \(0.795933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30.1948 | − | 12.7734i | −1.65466 | − | 0.699979i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1981 | − | 4.07579i | 0.611820 | − | 0.222684i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7434 | − | 11.5321i | 0.748650 | − | 0.628192i | −0.186496 | − | 0.982456i | \(-0.559713\pi\) |
0.935145 | + | 0.354264i | \(0.115269\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.785478 | + | 30.7127i | −0.0426613 | + | 1.66808i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.471996 | + | 0.272507i | −0.0255600 | + | 0.0147571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.47136 | − | 1.42684i | −0.133441 | − | 0.0770422i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −35.2753 | + | 5.29394i | −1.89916 | + | 0.285016i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.12290 | + | 17.7109i | 0.167646 | + | 0.950769i | 0.946294 | + | 0.323307i | \(0.104795\pi\) |
−0.778648 | + | 0.627461i | \(0.784094\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9984 | + | 14.2633i | 0.909901 | + | 0.763498i | 0.972100 | − | 0.234566i | \(-0.0753669\pi\) |
−0.0621990 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.817836 | − | 8.33354i | −0.0436529 | − | 0.444812i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.79906 | + | 11.6781i | −0.521551 | + | 0.621561i | −0.960947 | − | 0.276733i | \(-0.910748\pi\) |
0.439395 | + | 0.898294i | \(0.355193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1374 | + | 2.66914i | −0.803411 | + | 0.141663i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.916195 | + | 0.729688i | −0.0484902 | + | 0.0386192i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.52298 | − | 6.10199i | 0.185936 | − | 0.322051i | −0.757956 | − | 0.652306i | \(-0.773802\pi\) |
0.943892 | + | 0.330256i | \(0.107135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3734 | + | 24.8955i | 0.756495 | + | 1.31029i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.26889 | + | 2.07348i | −0.0665995 | + | 0.108830i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.7132 | − | 21.1098i | −0.927153 | − | 1.10494i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.13340 | − | 11.3564i | −0.215762 | − | 0.592800i | 0.783842 | − | 0.620961i | \(-0.213257\pi\) |
−0.999603 | + | 0.0281603i | \(0.991035\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.47133 | − | 1.02654i | −0.232768 | − | 0.0534395i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.126596 | + | 0.717963i | −0.00657255 | + | 0.0372748i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2735 | + | 5.19514i | 0.739056 | + | 0.268994i | 0.683993 | − | 0.729489i | \(-0.260242\pi\) |
0.0550629 | + | 0.998483i | \(0.482464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.54478 | + | 5.14326i | −0.234691 | + | 0.265597i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.79180i | 0.349796i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.4726i | 1.20571i | 0.797852 | + | 0.602853i | \(0.205969\pi\) | ||||
−0.797852 | + | 0.602853i | \(0.794031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.10961 | − | 1.44195i | −0.364236 | − | 0.0738732i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.57744 | − | 2.03002i | −0.284994 | − | 0.103729i | 0.195568 | − | 0.980690i | \(-0.437345\pi\) |
−0.480562 | + | 0.876961i | \(0.659567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.323507 | + | 1.83470i | −0.0164874 | + | 0.0935048i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.3490 | − | 17.0655i | −1.33940 | − | 0.867490i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.24510 | + | 17.1583i | 0.316639 | + | 0.869958i | 0.991275 | + | 0.131808i | \(0.0420783\pi\) |
−0.674636 | + | 0.738150i | \(0.735700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8851 | − | 17.7394i | −0.752771 | − | 0.897118i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.3199 | − | 20.8183i | −0.571011 | − | 1.05014i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0469 | − | 24.3299i | −0.706775 | − | 1.22417i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7443 | − | 22.0738i | 0.639620 | − | 1.10785i | −0.345897 | − | 0.938273i | \(-0.612425\pi\) |
0.985516 | − | 0.169581i | \(-0.0542414\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.27715 | + | 0.895387i | 0.114000 | + | 0.0448254i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3971 | − | 5.18350i | 1.46802 | − | 0.258852i | 0.618240 | − | 0.785989i | \(-0.287846\pi\) |
0.849780 | + | 0.527138i | \(0.176735\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.182242 | + | 0.217187i | −0.00907811 | + | 0.0108189i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.4560 | + | 15.5088i | 1.06616 | + | 0.770638i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.9340 | − | 21.7612i | −1.28550 | − | 1.07866i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.05387 | + | 28.6619i | 0.249898 | + | 1.41724i | 0.808838 | + | 0.588032i | \(0.200097\pi\) |
−0.558940 | + | 0.829208i | \(0.688792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.299816 | + | 0.762492i | −0.0147888 | + | 0.0376110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.885476 | − | 0.511230i | −0.0435714 | − | 0.0251560i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.1682 | − | 16.2629i | 1.38272 | − | 0.798315i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.4206 | − | 17.6286i | 1.58765 | − | 0.863277i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.66441 | − | 3.07481i | 0.179018 | − | 0.150214i | −0.548875 | − | 0.835904i | \(-0.684944\pi\) |
0.727894 | + | 0.685690i | \(0.240499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1855 | − | 6.25501i | 0.837570 | − | 0.304851i | 0.112608 | − | 0.993639i | \(-0.464079\pi\) |
0.724962 | + | 0.688789i | \(0.241857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.8479 | − | 27.0962i | −0.673308 | − | 1.31746i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.8988 | + | 2.09809i | 0.577178 | + | 0.101772i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.475575 | − | 1.30663i | 0.0230147 | − | 0.0632323i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.71869 | − | 8.47409i | 0.0829789 | − | 0.409133i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9894 | −0.770181 | −0.385091 | − | 0.922879i | \(-0.625830\pi\) | ||||
−0.385091 | + | 0.922879i | \(0.625830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0614 | −0.916031 | −0.458016 | − | 0.888944i | \(-0.651440\pi\) | ||||
−0.458016 | + | 0.888944i | \(0.651440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.0912 | − | 14.2188i | −0.771512 | − | 0.681737i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.5459 | + | 45.4594i | −0.791497 | + | 2.17462i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.2264 | + | 3.74279i | 1.01308 | + | 0.178634i | 0.655458 | − | 0.755232i | \(-0.272476\pi\) |
0.357625 | + | 0.933865i | \(0.383587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.9550 | + | 6.12751i | −0.950239 | + | 0.291786i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7234 | − | 4.99490i | 0.652018 | − | 0.237315i | 0.00523142 | − | 0.999986i | \(-0.498335\pi\) |
0.646786 | + | 0.762671i | \(0.276113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.89486 | + | 5.78547i | −0.326848 | + | 0.274258i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.4438 | − | 17.4065i | −1.34535 | − | 0.823300i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.2978 | + | 10.5643i | −0.863528 | + | 0.498558i | −0.865192 | − | 0.501440i | \(-0.832804\pi\) |
0.00166397 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.10258 | − | 2.36863i | −0.193183 | − | 0.111534i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.2892 | + | 16.6859i | 0.624380 | + | 0.783970i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.168289 | + | 0.954414i | 0.00788951 | + | 0.0447436i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.17150 | − | 0.983008i | −0.0548006 | − | 0.0459832i | 0.614976 | − | 0.788546i | \(-0.289166\pi\) |
−0.669777 | + | 0.742563i | \(0.733610\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.31709 | + | 17.1364i | −0.0614766 | + | 0.799861i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.11059 | − | 10.8576i | 0.424322 | − | 0.505688i | −0.510953 | − | 0.859609i | \(-0.670707\pi\) |
0.935275 | + | 0.353921i | \(0.115152\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.5679 | + | 6.27159i | −1.65298 | + | 0.291465i | −0.920914 | − | 0.389766i | \(-0.872556\pi\) |
−0.732068 | + | 0.681231i | \(0.761445\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.133035 | − | 0.886453i | −0.00616933 | − | 0.0411083i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2029 | + | 22.8680i | −0.610956 | + | 1.05821i | 0.380124 | + | 0.924936i | \(0.375881\pi\) |
−0.991080 | + | 0.133271i | \(0.957452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.414120 | − | 0.717276i | −0.0191223 | − | 0.0331207i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.7026 | + | 0.708495i | 1.27647 | + | 0.0326457i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.8368 | − | 24.8324i | −0.958078 | − | 1.14179i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.63295 | − | 23.7188i | −0.396107 | − | 1.08829i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.44855 | + | 8.53581i | 0.295259 | + | 0.390828i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.459687 | + | 2.60701i | −0.0210036 | + | 0.119117i | −0.993507 | − | 0.113772i | \(-0.963707\pi\) |
0.972503 | + | 0.232889i | \(0.0748179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.5491 | − | 6.02338i | −0.754574 | − | 0.274643i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.788080 | + | 2.35055i | 0.0358589 | + | 0.106954i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.96693i | − | 0.225537i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.95003i | − | 0.450879i | −0.974257 | − | 0.225440i | \(-0.927618\pi\) | ||
0.974257 | − | 0.225440i | \(-0.0723818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.89458 | + | 20.5640i | 0.311784 | + | 0.929936i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7065 | + | 7.17257i | 0.889341 | + | 0.323694i | 0.745973 | − | 0.665976i | \(-0.231985\pi\) |
0.143368 | + | 0.989669i | \(0.454207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.42072 | − | 13.7286i | 0.109024 | − | 0.618303i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.4787 | + | 21.8126i | 0.740664 | + | 0.980402i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.365383 | + | 1.00388i | 0.0163897 | + | 0.0450302i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.59699 | + | 5.47848i | 0.205789 | + | 0.245250i | 0.859061 | − | 0.511874i | \(-0.171048\pi\) |
−0.653271 | + | 0.757124i | \(0.726604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.1734 | − | 0.285759i | −0.499189 | − | 0.0127668i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.12080 | + | 3.67334i | 0.0945619 | + | 0.163786i | 0.909426 | − | 0.415866i | \(-0.136522\pi\) |
−0.814864 | + | 0.579653i | \(0.803188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9259 | − | 18.9243i | 0.486198 | − | 0.842119i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67421 | + | 17.8191i | 0.118766 | + | 0.791375i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.9453 | − | 6.33812i | 1.59325 | − | 0.280932i | 0.694530 | − | 0.719463i | \(-0.255612\pi\) |
0.898716 | + | 0.438531i | \(0.144501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.23110 | + | 1.46717i | −0.0544607 | + | 0.0649037i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.3789 | − | 15.5168i | 1.42956 | − | 0.685083i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.5866 | + | 30.6998i | 1.61220 | + | 1.35280i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.45637 | − | 30.9446i | −0.239971 | − | 1.36094i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.24184 | − | 5.32605i | −0.186196 | − | 0.233788i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7979 | − | 12.0077i | −0.911174 | − | 0.526067i | −0.0303652 | − | 0.999539i | \(-0.509667\pi\) |
−0.880809 | + | 0.473472i | \(0.843000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.54766 | + | 2.04824i | −0.155128 | + | 0.0895633i | −0.575555 | − | 0.817763i | \(-0.695214\pi\) |
0.420426 | + | 0.907327i | \(0.361880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.10332 | − | 0.675187i | −0.0481527 | − | 0.0294676i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.445783 | − | 0.374056i | 0.0194186 | − | 0.0162941i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.4464 | + | 8.89776i | −1.06289 | + | 0.386859i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.3425 | + | 4.40410i | −0.622412 | + | 0.191122i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.42689 | − | 0.427927i | −0.105120 | − | 0.0185356i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.4807 | + | 37.0379i | −0.582820 | + | 1.60129i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.3503 | + | 30.3532i | 1.48233 | + | 1.30984i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.5553 | −0.928451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7933 | −1.23792 | −0.618960 | − | 0.785423i | \(-0.712446\pi\) | ||||
−0.618960 | + | 0.785423i | \(0.712446\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.90909 | + | 9.41289i | −0.0819269 | + | 0.403946i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.7267 | + | 40.4613i | −0.630823 | + | 1.73317i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0427 | + | 5.64999i | 1.37005 | + | 0.241576i | 0.809778 | − | 0.586736i | \(-0.199587\pi\) |
0.560267 | + | 0.828312i | \(0.310698\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.28535 | − | 18.1687i | −0.396289 | − | 0.775419i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.3662 | + | 9.96047i | −1.16584 | + | 0.424330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.49575 | + | 1.25509i | −0.0636059 | + | 0.0533716i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 48.9164 | − | 26.5981i | 2.07639 | − | 1.12903i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.09638 | − | 1.21034i | 0.0888264 | − | 0.0512840i | −0.454929 | − | 0.890528i | \(-0.650335\pi\) |
0.543755 | + | 0.839244i | \(0.317002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6039 | − | 8.43154i | −0.617677 | − | 0.356616i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.49437 | + | 16.5165i | −0.274192 | + | 0.697326i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.64509 | − | 37.6862i | −0.280057 | − | 1.58828i | −0.722426 | − | 0.691449i | \(-0.756973\pi\) |
0.442369 | − | 0.896833i | \(-0.354138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.9699 | − | 33.5388i | −1.68155 | − | 1.41099i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.802563 | − | 1.65575i | 0.0337045 | − | 0.0695349i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.36673 | − | 4.01232i | 0.141141 | − | 0.168205i | −0.690843 | − | 0.723005i | \(-0.742761\pi\) |
0.831984 | + | 0.554799i | \(0.187205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.6895 | − | 4.52974i | 1.07507 | − | 0.189564i | 0.392036 | − | 0.919950i | \(-0.371771\pi\) |
0.683034 | + | 0.730386i | \(0.260660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1883 | − | 5.97212i | −0.634500 | − | 0.249489i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.7871 | − | 22.1479i | 0.533258 | − | 0.923629i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.175577 | + | 0.304109i | 0.00730939 | + | 0.0126602i | 0.869657 | − | 0.493657i | \(-0.164340\pi\) |
−0.862348 | + | 0.506317i | \(0.831007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.4147 | + | 24.6709i | 0.557497 | + | 1.02529i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.45309 | − | 1.73172i | −0.0602842 | − | 0.0718439i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.77818 | + | 10.3805i | 0.156476 | + | 0.429915i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.9362 | + | 7.73076i | 0.493501 | + | 0.319627i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.48582 | + | 8.42649i | −0.0613262 | + | 0.347798i | 0.938669 | + | 0.344819i | \(0.112060\pi\) |
−0.999996 | + | 0.00297975i | \(0.999052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.14238 | − | 0.415791i | −0.0470708 | − | 0.0171324i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.4867 | − | 4.96631i | −1.00725 | − | 0.204287i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 0.724041i | − | 0.0297328i | −0.999889 | − | 0.0148664i | \(-0.995268\pi\) | ||
0.999889 | − | 0.0148664i | \(-0.00473230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.98918i | − | 0.0815484i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.46718 | + | 5.05544i | −0.182829 | + | 0.206905i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.8615 | + | 13.7805i | 1.54698 | + | 0.563055i | 0.967707 | − | 0.252078i | \(-0.0811140\pi\) |
0.579274 | + | 0.815133i | \(0.303336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.501839 | + | 2.84607i | −0.0204704 | + | 0.116094i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) |
0.972860 | + | 0.231393i | \(0.0743284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.8453 | − | 2.71948i | −0.482379 | − | 0.110746i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.41203 | − | 3.87951i | −0.0574071 | − | 0.157725i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3491 | + | 17.1005i | 0.582410 | + | 0.694089i | 0.974128 | − | 0.225996i | \(-0.0725636\pi\) |
−0.391718 | + | 0.920085i | \(0.628119\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.779013 | + | 1.27298i | −0.0315672 | + | 0.0515836i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.17290 | − | 14.1559i | −0.330640 | − | 0.572686i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4658 | − | 26.7875i | 0.624657 | − | 1.08194i | −0.363950 | − | 0.931419i | \(-0.618572\pi\) |
0.988607 | − | 0.150520i | \(-0.0480946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.09458 | − | 4.85393i | 0.245757 | − | 0.195729i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.0462 | + | 4.94530i | −1.12910 | + | 0.199090i | −0.706831 | − | 0.707382i | \(-0.749876\pi\) |
−0.422265 | + | 0.906472i | \(0.638765\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.86139 | + | 8.17709i | −0.275783 | + | 0.328665i | −0.886102 | − | 0.463491i | \(-0.846597\pi\) |
0.610319 | + | 0.792156i | \(0.291041\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.1308 | + | 15.0254i | 1.32949 | + | 0.602947i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.479205 | + | 0.402100i | 0.0191989 | + | 0.0161098i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.19570 | − | 29.4663i | −0.207828 | − | 1.17865i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 36.6651 | − | 5.50252i | 1.46426 | − | 0.219750i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.3046 | + | 18.0737i | 1.24820 | + | 0.720646i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.930324 | + | 0.537123i | −0.0370356 | + | 0.0213825i | −0.518403 | − | 0.855136i | \(-0.673473\pi\) |
0.481368 | + | 0.876519i | \(0.340140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.908423 | − | 35.5199i | 0.0361066 | − | 1.41179i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.43784 | − | 7.91929i | 0.374529 | − | 0.314267i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5369 | + | 3.83511i | −0.417486 | + | 0.151953i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.4375 | + | 6.10757i | 0.571139 | + | 0.241612i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.2400 | − | 2.51090i | −0.562448 | − | 0.0991748i | −0.114807 | − | 0.993388i | \(-0.536625\pi\) |
−0.447642 | + | 0.894213i | \(0.647736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.89665 | − | 24.4433i | 0.350850 | − | 0.963951i | −0.631248 | − | 0.775581i | \(-0.717457\pi\) |
0.982098 | − | 0.188371i | \(-0.0603206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 50.5494 | − | 16.9479i | 1.99038 | − | 0.667324i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.7872 | 1.60351 | 0.801754 | − | 0.597654i | \(-0.203900\pi\) | ||||
0.801754 | + | 0.597654i | \(0.203900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4927 | −0.608141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0590685 | + | 0.0198041i | −0.00231508 | + | 0.000776186i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.910599 | − | 2.50185i | 0.0356345 | − | 0.0979050i | −0.920599 | − | 0.390508i | \(-0.872299\pi\) |
0.956234 | + | 0.292603i | \(0.0945215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.6334 | + | 6.98843i | 1.54860 | + | 0.273061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.45910 | + | 27.8905i | 0.134952 | + | 1.08811i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.60227 | + | 1.67509i | −0.179279 | + | 0.0652522i | −0.430100 | − | 0.902781i | \(-0.641522\pi\) |
0.250821 | + | 0.968033i | \(0.419299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.04237 | + | 0.874649i | −0.0405434 | + | 0.0340199i | −0.662834 | − | 0.748766i | \(-0.730647\pi\) |
0.622291 | + | 0.782786i | \(0.286202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.236038 | + | 9.22924i | −0.00916695 | + | 0.358434i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.59881 | + | 2.07777i | −0.139556 | + | 0.0805726i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.5536 | − | 14.7534i | −0.989440 | − | 0.571253i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.77275 | + | 1.31657i | −0.339174 | + | 0.0509016i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.65863 | − | 20.7491i | −0.141240 | − | 0.801010i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.96510 | + | 5.00532i | 0.229938 | + | 0.192941i | 0.750476 | − | 0.660898i | \(-0.229824\pi\) |
−0.520538 | + | 0.853838i | \(0.674269\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.2813 | + | 5.10592i | −0.703646 | + | 0.196527i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.5599 | + | 36.4198i | −1.17451 | + | 1.39973i | −0.275783 | + | 0.961220i | \(0.588937\pi\) |
−0.898727 | + | 0.438508i | \(0.855507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.339966 | + | 0.0599452i | −0.0130467 | + | 0.00230048i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.81713 | + | 3.04009i | −0.146273 | + | 0.116496i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.48629 | + | 2.57432i | −0.0568712 | + | 0.0985037i | −0.893059 | − | 0.449939i | \(-0.851446\pi\) |
0.836188 | + | 0.548443i | \(0.184779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.695733 | − | 1.20505i | −0.0265826 | − | 0.0460424i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.40827 | + | 13.7399i | −0.320795 | + | 0.524209i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.69378 | + | 4.40208i | 0.140722 | + | 0.167706i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.9301 | + | 41.0201i | 0.567967 | + | 1.56048i | 0.807672 | + | 0.589632i | \(0.200727\pi\) |
−0.239705 | + | 0.970846i | \(0.577051\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.29410 | − | 1.39115i | 0.0491588 | − | 0.0528456i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.8832 | + | 61.7217i | −0.412824 | + | 2.34124i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.75306 | + | 1.72997i | 0.180035 | + | 0.0655274i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.0943 | − | 30.6622i | 1.02480 | − | 1.15975i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.5239i | 1.79495i | 0.441063 | + | 0.897476i | \(0.354602\pi\) | ||||
−0.441063 | + | 0.897476i | \(0.645398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 75.5147i | − | 2.84809i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.6482 | + | 10.2723i | 1.90752 | + | 0.386877i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.42715 | − | 0.519441i | −0.0536735 | − | 0.0195356i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.48937 | + | 8.44661i | −0.0559343 | + | 0.317219i | −0.999918 | − | 0.0127717i | \(-0.995935\pi\) |
0.943984 | + | 0.329991i | \(0.107046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.46458 | + | 28.6143i | −0.0549260 | + | 1.07312i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.421278 | − | 1.15745i | −0.0157770 | − | 0.0433469i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.43916 | + | 11.2492i | 0.353005 | + | 0.420695i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.3043 | + | 28.1460i | 0.571548 | + | 1.05113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5537 | + | 20.0116i | 0.430881 | + | 0.746308i | 0.996949 | − | 0.0780505i | \(-0.0248695\pi\) |
−0.566068 | + | 0.824358i | \(0.691536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.65972 | − | 2.87471i | 0.0618111 | − | 0.107060i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.90299 | + | 1.92788i | 0.182344 | + | 0.0716987i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.1615 | − | 2.67338i | 0.563084 | − | 0.0992870i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.97816 | − | 9.50800i | 0.295893 | − | 0.352632i | −0.597531 | − | 0.801846i | \(-0.703851\pi\) |
0.893424 | + | 0.449214i | \(0.148296\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.76820 | − | 25.1711i | −0.361785 | − | 0.932261i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.5143 | + | 22.2481i | 0.980665 | + | 0.822876i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.42442 | − | 8.07829i | −0.0526122 | − | 0.298379i | 0.947136 | − | 0.320833i | \(-0.103963\pi\) |
−0.999748 | + | 0.0224548i | \(0.992852\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.9730 | − | 32.9929i | 0.478516 | − | 1.21696i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.8684 | − | 6.27489i | −0.400344 | − | 0.231139i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6088 | + | 14.7852i | −0.942034 | + | 0.543884i | −0.890597 | − | 0.454793i | \(-0.849713\pi\) |
−0.0514367 | + | 0.998676i | \(0.516380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.9440 | − | 9.21325i | 0.622454 | − | 0.338457i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1792 | − | 18.6105i | 0.813675 | − | 0.682754i | −0.137807 | − | 0.990459i | \(-0.544005\pi\) |
0.951482 | + | 0.307705i | \(0.0995610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.2188 | − | 19.3701i | 1.94979 | − | 0.709664i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −33.1285 | − | 1.69563i | −1.21211 | − | 0.0620399i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.69778 | + | 0.475692i | 0.0985749 | + | 0.0173814i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6007 | + | 37.3675i | −0.496295 | + | 1.36356i | 0.398536 | + | 0.917153i | \(0.369518\pi\) |
−0.894831 | + | 0.446406i | \(0.852704\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.910845 | + | 4.49098i | −0.0331930 | + | 0.163660i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.2272 | −1.31844 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.11133 | 0.294811 | 0.147406 | − | 0.989076i | \(-0.452908\pi\) | ||||
0.147406 | + | 0.989076i | \(0.452908\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.1497 | + | 24.8741i | 1.02177 | + | 0.902873i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.2460 | + | 30.8982i | −0.407668 | + | 1.12006i | 0.550744 | + | 0.834674i | \(0.314344\pi\) |
−0.958413 | + | 0.285386i | \(0.907878\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.94714 | + | 0.519661i | 0.106694 | + | 0.0188130i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.3718 | − | 19.8808i | −0.772699 | − | 0.718791i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.57330 | + | 2.75646i | −0.273456 | + | 0.0995299i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.60501 | − | 4.70316i | 0.202122 | − | 0.169600i | −0.536109 | − | 0.844149i | \(-0.680106\pi\) |
0.738230 | + | 0.674549i | \(0.235662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0920 | − | 13.5194i | −0.795623 | − | 0.486890i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.5895 | + | 17.6608i | −1.10023 | + | 0.635216i | −0.936281 | − | 0.351253i | \(-0.885756\pi\) |
−0.163946 | + | 0.986469i | \(0.552422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.556567 | + | 0.321334i | 0.0199925 | + | 0.0115427i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.41090 | − | 3.02712i | −0.0864905 | − | 0.108597i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.83490 | − | 10.4062i | −0.0657421 | − | 0.372842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4003 | + | 10.4051i | 0.443716 | + | 0.372322i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.89107 | + | 21.0924i | 0.210530 | + | 0.753782i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.2517 | + | 36.0526i | −1.07973 | + | 1.28677i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2798 | − | 1.81261i | 0.366437 | − | 0.0646127i | 0.0126019 | − | 0.999921i | \(-0.495989\pi\) |
0.353835 | + | 0.935308i | \(0.384877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.09384 | − | 40.6052i | −0.216946 | − | 1.44558i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.81320 | + | 3.14055i | −0.0644699 | + | 0.111665i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.48013 | − | 9.49186i | −0.194605 | − | 0.337066i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.1624 | − | 0.464504i | −0.644155 | − | 0.0164743i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6780 | − | 35.3688i | −1.05125 | − | 1.25283i | −0.966565 | − | 0.256420i | \(-0.917457\pi\) |
−0.0846822 | − | 0.996408i | \(-0.526988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.4748 | + | 31.5269i | 0.405951 | + | 1.11534i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.10956 | − | 1.12981i | 0.321871 | − | 0.0399197i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.03937 | + | 28.5797i | −0.177836 | + | 1.00856i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.95647 | − | 1.44004i | −0.139447 | − | 0.0507547i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.90879 | − | 29.5543i | −0.348806 | − | 1.04036i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 11.2600i | − | 0.395879i | −0.980214 | − | 0.197940i | \(-0.936575\pi\) | ||
0.980214 | − | 0.197940i | \(-0.0634250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.9559i | − | 0.595402i | −0.954659 | − | 0.297701i | \(-0.903780\pi\) | ||
0.954659 | − | 0.297701i | \(-0.0962199\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.79406 | − | 11.3163i | −0.133064 | − | 0.396880i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.6135 | − | 12.5983i | −1.21246 | − | 0.441298i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5560 | − | 71.2084i | 0.439278 | − | 2.49127i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.385082 | − | 0.910285i | 0.0134559 | − | 0.0318079i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2073 | + | 47.2768i | 0.600540 | + | 1.64997i | 0.750183 | + | 0.661231i | \(0.229966\pi\) |
−0.149642 | + | 0.988740i | \(0.547812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.76846 | + | 6.87459i | 0.201076 | + | 0.239633i | 0.857154 | − | 0.515060i | \(-0.172230\pi\) |
−0.656078 | + | 0.754693i | \(0.727786\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.5934 | − | 0.501102i | −0.682155 | − | 0.0174461i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.8689 | − | 36.1460i | −0.725683 | − | 1.25692i | −0.958692 | − | 0.284445i | \(-0.908191\pi\) |
0.233009 | − | 0.972474i | \(-0.425143\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2998 | + | 38.6243i | −0.774503 | + | 1.34148i | 0.160570 | + | 0.987024i | \(0.448667\pi\) |
−0.935073 | + | 0.354454i | \(0.884667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.39165 | + | 9.27303i | 0.0482758 | + | 0.321678i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.6656 | − | 3.99655i | 0.785315 | − | 0.138472i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2015 | − | 14.5412i | 0.422250 | − | 0.503219i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.377582 | + | 0.832564i | −0.0130511 | + | 0.0287776i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.9701 | − | 18.4351i | −0.758493 | − | 0.636451i | 0.179241 | − | 0.983805i | \(-0.442636\pi\) |
−0.937734 | + | 0.347354i | \(0.887080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.95132 | + | 11.0665i | 0.0672868 | + | 0.381603i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.0869 | − | 23.9655i | −0.657387 | − | 0.825414i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.5016 | − | 15.3007i | −0.911684 | − | 0.526361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.248495 | + | 0.143469i | −0.00853839 | + | 0.00492964i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.15978 | + | 5.60543i | 0.314363 | + | 0.192378i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.6110 | − | 49.1805i | 2.00916 | − | 1.68589i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5794 | + | 8.58220i | −0.807344 | + | 0.293849i | −0.712526 | − | 0.701646i | \(-0.752449\pi\) |
−0.0948175 | + | 0.995495i | \(0.530227\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.6445 | + | 59.4319i | −0.466633 | + | 2.03253i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1757 | + | 2.67588i | 0.518391 | + | 0.0914062i | 0.426721 | − | 0.904383i | \(-0.359669\pi\) |
0.0916694 | + | 0.995789i | \(0.470780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0508180 | + | 0.139621i | −0.00173389 | + | 0.00476382i | −0.940557 | − | 0.339637i | \(-0.889696\pi\) |
0.938823 | + | 0.344401i | \(0.111918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.405786 | − | 0.358568i | −0.0138291 | − | 0.0122200i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0868 | −0.377401 | −0.188700 | − | 0.982035i | \(-0.560427\pi\) | ||||
−0.188700 | + | 0.982035i | \(0.560427\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5636 | 0.393173 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.08617 | + | 10.2860i | −0.0708501 | + | 0.349331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1190 | + | 27.8017i | −0.343264 | + | 0.943110i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.42925 | − | 1.13365i | −0.217847 | − | 0.0384123i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.75372 | + | 4.25172i | −0.0931994 | + | 0.143899i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.761288 | + | 0.277086i | −0.0257362 | + | 0.00936722i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9804 | + | 12.5701i | −0.505853 | + | 0.424461i | −0.859667 | − | 0.510855i | \(-0.829329\pi\) |
0.353814 | + | 0.935316i | \(0.384885\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.6402 | − | 10.6793i | 0.662447 | − | 0.360203i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6073 | − | 6.70150i | 0.391061 | − | 0.225779i | −0.291559 | − | 0.956553i | \(-0.594174\pi\) |
0.682620 | + | 0.730774i | \(0.260841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.2283 | − | 24.3805i | −1.42109 | − | 0.820469i | −0.424702 | − | 0.905333i | \(-0.639621\pi\) |
−0.996393 | + | 0.0848644i | \(0.972954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.32423 | − | 23.7134i | 0.313431 | − | 0.797116i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.57423 | + | 14.5992i | 0.0864342 | + | 0.490193i | 0.997038 | + | 0.0769121i | \(0.0245061\pi\) |
−0.910604 | + | 0.413281i | \(0.864383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.655946 | − | 0.550404i | −0.0219997 | − | 0.0184600i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.01275 | − | 27.8077i | −0.0674297 | − | 0.931591i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.0523 | − | 53.6912i | 1.50762 | − | 1.79671i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −76.6675 | + | 13.5185i | −2.56271 | + | 0.451875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.1860 | + | 7.15085i | 0.607214 | + | 0.238760i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.370747 | − | 0.642152i | 0.0123651 | − | 0.0214170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.89743 | − | 10.2146i | −0.196472 | − | 0.340299i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.77009 | − | 3.25536i | −0.0589049 | − | 0.108332i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.4849 | − | 12.4954i | −0.348529 | − | 0.415361i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.70905 | − | 12.9380i | −0.156361 | − | 0.429599i | 0.836633 | − | 0.547764i | \(-0.184521\pi\) |
−0.992994 | + | 0.118165i | \(0.962299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.8445 | + | 10.1418i | −0.658200 | + | 0.336382i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.63552 | + | 9.27547i | −0.0541871 | + | 0.307310i | −0.999840 | − | 0.0178664i | \(-0.994313\pi\) |
0.945653 | + | 0.325177i | \(0.105424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.1877 | − | 11.7154i | −1.06526 | − | 0.387722i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.9609 | + | 6.88783i | 1.12271 | + | 0.227705i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.79708i | − | 0.0923678i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 9.65673i | − | 0.318546i | −0.987235 | − | 0.159273i | \(-0.949085\pi\) | ||
0.987235 | − | 0.159273i | \(-0.0509150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5141 | + | 18.6888i | −0.544160 | + | 0.615818i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.91290 | + | 2.88006i | 0.260456 | + | 0.0947983i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93210 | + | 39.3139i | −0.227926 | + | 1.29263i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.2980 | − | 46.5632i | −0.469608 | − | 1.52934i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.6393 | − | 53.9586i | −0.644345 | − | 1.77032i | −0.637626 | − | 0.770346i | \(-0.720084\pi\) |
−0.00671888 | − | 0.999977i | \(-0.502139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.9056 | − | 36.8318i | −1.01289 | − | 1.20711i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.94867 | + | 11.3548i | −0.227489 | + | 0.371738i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.0704 | − | 26.1027i | −0.492855 | − | 0.853649i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1261 | − | 24.4672i | 0.461481 | − | 0.799308i | −0.537554 | − | 0.843229i | \(-0.680652\pi\) |
0.999035 | + | 0.0439213i | \(0.0139851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.81629 | + | 7.02159i | −0.287709 | + | 0.229141i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7390 | − | 2.06991i | 0.382682 | − | 0.0674771i | 0.0210018 | − | 0.999779i | \(-0.493314\pi\) |
0.361680 | + | 0.932302i | \(0.382203\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.88182 | − | 8.20143i | 0.224103 | − | 0.267075i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.35047 | + | 2.81803i | 0.0439309 | + | 0.0916706i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.50552 | + | 3.78058i | 0.146410 | + | 0.122852i | 0.713051 | − | 0.701112i | \(-0.247313\pi\) |
−0.566641 | + | 0.823965i | \(0.691757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.62150 | + | 14.8672i | 0.0850974 | + | 0.482611i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.5107 | + | 5.02912i | −1.08666 | + | 0.163080i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1113 | + | 6.41508i | 0.359929 | + | 0.207805i | 0.669050 | − | 0.743218i | \(-0.266701\pi\) |
−0.309121 | + | 0.951023i | \(0.600035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0036 | − | 13.8585i | 0.776739 | − | 0.448451i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.578159 | + | 22.6064i | −0.0186892 | + | 0.730760i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0740836 | + | 0.0621636i | −0.00239229 | + | 0.00200737i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1014 | + | 10.5920i | −0.938754 | + | 0.341679i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.0737 | − | 24.2307i | 1.03356 | − | 0.780825i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.9680 | − | 8.28173i | −1.51195 | − | 0.266598i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.81601 | + | 24.2218i | −0.283504 | + | 0.778920i | 0.713434 | + | 0.700722i | \(0.247139\pi\) |
−0.996938 | + | 0.0781978i | \(0.975083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.5335 | + | 12.5840i | −1.20575 | + | 0.404256i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.8706 | −1.63252 | −0.816258 | − | 0.577688i | \(-0.803955\pi\) | ||||
−0.816258 | + | 0.577688i | \(0.803955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.35595 | 0.139645 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.66703 | + | 3.24110i | −0.309593 | + | 0.103798i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.82686 | − | 16.0092i | 0.186418 | − | 0.512179i | −0.810915 | − | 0.585164i | \(-0.801030\pi\) |
0.997333 | + | 0.0729849i | \(0.0232525\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.33467 | + | 1.64595i | 0.298337 | + | 0.0526049i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.0384 | − | 26.4704i | 1.11869 | − | 0.845136i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.8917 | + | 16.3393i | −1.43182 | + | 0.521141i | −0.937454 | − | 0.348110i | \(-0.886824\pi\) |
−0.494370 | + | 0.869251i | \(0.664601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.5056 | − | 27.2754i | 1.03571 | − | 0.869067i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0918306 | − | 3.59064i | 0.00292300 | − | 0.114291i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.4460 | − | 36.6306i | 2.01746 | − | 1.16478i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.398267 | − | 0.229939i | −0.0126514 | − | 0.00730427i | 0.493661 | − | 0.869654i | \(-0.335658\pi\) |
−0.506312 | + | 0.862350i | \(0.668992\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.7188 | + | 6.41104i | −1.35564 | + | 0.203448i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.98957 | − | 11.2834i | −0.0630735 | − | 0.357708i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.01787 | − | 1.69320i | −0.0639067 | − | 0.0536241i | 0.610275 | − | 0.792190i | \(-0.291059\pi\) |
−0.674182 | + | 0.738566i | \(0.735503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −56.6190 | − | 4.35169i | −1.79135 | − | 0.137681i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.be.a.335.6 | yes | 36 | |
4.3 | odd | 2 | inner | 432.2.be.a.335.1 | ✓ | 36 | |
27.5 | odd | 18 | inner | 432.2.be.a.383.1 | yes | 36 | |
108.59 | even | 18 | inner | 432.2.be.a.383.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.a.335.1 | ✓ | 36 | 4.3 | odd | 2 | inner | |
432.2.be.a.335.6 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.a.383.1 | yes | 36 | 27.5 | odd | 18 | inner | |
432.2.be.a.383.6 | yes | 36 | 108.59 | even | 18 | inner |